## [0] flags are bits $${\frac{{{f_{0}\left(x\right)}}^{{2}} - {f_{0}\left(x\right)}}{{x}^{{\frac{T}{{2}}}} - {1}}}$$

## [1] flags_extra are bits $${\frac{{{f_{0}\left(xg^{3}\right)}}^{{2}} - {f_{0}\left(xg^{3}\right)}}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [2] instruction format $${\frac{{f_{4}\left(xg^{3}\right)} - \left(\left(\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{1}\left(xg^{11}\right)} \cdot 2^{192}+{f_{1}\left(xg^{10}\right)} \cdot 2^{176}+{f_{1}\left(xg^{9}\right)} \cdot 2^{160}+{f_{1}\left(xg^{8}\right)} \cdot 2^{144}+{f_{1}\left(xg^{7}\right)} \cdot 2^{128}+{f_{1}\left(xg^{6}\right)} \cdot 2^{112}+{f_{1}\left(xg^{5}\right)} \cdot 2^{96}+{f_{1}\left(xg^{4}\right)} \cdot 2^{80}+{f_{1}\left(xg^{3}\right)} \cdot 2^{64}+{f_{1}\left(xg^{2}\right)} \cdot 2^{48}+{f_{1}\left(xg\right)} \cdot 2^{32}+{f_{1}\left(x\right)} \cdot 2^{16}\right) + {f_{0}\left(xg^{4}\right)} \cdot \left({f_{1}\left(xg^{15}\right)} \cdot 2^{240}+{f_{1}\left(xg^{14}\right)} \cdot 2^{224}+{f_{1}\left(xg^{13}\right)} \cdot 2^{208}+{f_{1}\left(xg^{12}\right)} \cdot 2^{192}+{f_{1}\left(xg^{10}\right)} \cdot 2^{176}+{f_{1}\left(xg^{9}\right)} \cdot 2^{160}+{f_{1}\left(xg^{8}\right)} \cdot 2^{144}+{f_{1}\left(xg^{7}\right)} \cdot 2^{128}+{f_{1}\left(xg^{6}\right)} \cdot 2^{112}+{f_{1}\left(xg^{5}\right)} \cdot 2^{96}+{f_{1}\left(xg^{4}\right)} \cdot 2^{80}+{f_{1}\left(xg^{3}\right)} \cdot 2^{64}+{f_{1}\left(xg^{2}\right)} \cdot 2^{48}+{f_{1}\left(xg\right)} \cdot 2^{32}+{f_{1}\left(x\right)} \cdot 2^{16}\right)\right) \cdot 2^{251}+{f_{0}\left(xg^{15}\right)} \cdot 2^{11}+{f_{0}\left(xg^{11}\right)} \cdot 2^{10}+{f_{0}\left(xg^{7}\right)} \cdot 2^{9}+{f_{0}\left(xg^{3}\right)} \cdot 2^{8}+{f_{0}\left(xg^{12}\right)} \cdot 2^{7}+{f_{0}\left(xg^{10}\right)} \cdot 2^{6}+{f_{0}\left(xg^{8}\right)} \cdot 2^{5}+{f_{0}\left(xg^{6}\right)} \cdot 2^{4}+{f_{0}\left(xg^{4}\right)} \cdot 2^{3}+{f_{0}\left(xg^{2}\right)} \cdot 2^{2}+{f_{0}\left(x\right)} \cdot 2^{1}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [3] inst_final $${\frac{{f_{4}\left(xg^{3}\right)} - {\mathrm{4001c00040004000c0014000400040014000400040004000000}_{16}}}{{x}^{{\frac{T}{T}}} - {g}^{T - {16}}}}$$

## [4] op1_base_addr $${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{4}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(x\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [5] op1_addr $${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{5}\right)} - \left({f_{4}\left(xg^{4}\right)} + {f_{1}\left(xg\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [6] op2_base_addr $${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{6}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{3}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [7] op2_addr $${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{7}\right)} - \left({f_{4}\left(xg^{6}\right)} + {f_{1}\left(xg^{4}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [8] dst_base_addr $${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{8}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{6}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [9] dst_addr $${\frac{\left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{3}\left(xg^{9}\right)} - \left({f_{4}\left(xg^{8}\right)} + {f_{1}\left(xg^{7}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [10] v1_op1_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{4}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(x\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [11] v1_op2_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{5}\right)} - \left({f_{3}\left(xg^{3}\right)} + {f_{1}\left(xg\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [12] v1_dst_base_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{6}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{2}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [13] v1_dst_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{7}\right)} - \left({f_{4}\left(xg^{6}\right)} + {f_{1}\left(xg^{3}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [14] v1_sum $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{4}\left(xg^{4}\right)} + {f_{4}\left(xg^{5}\right)} - \left({f_{4}\left(xg^{7}\right)} + {f_{1}\left(xg^{4}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [15] v2_op1_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{8}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{5}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [16] v2_op2_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{9}\right)} - \left({f_{3}\left(xg^{3}\right)} + {f_{1}\left(xg^{6}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [17] v2_dst_base_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{10}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{7}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [18] v2_dst_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{11}\right)} - \left({f_{4}\left(xg^{10}\right)} + {f_{1}\left(xg^{8}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [19] v2_sum $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{4}\left(xg^{8}\right)} + {f_{4}\left(xg^{9}\right)} - \left({f_{4}\left(xg^{11}\right)} + {f_{1}\left(xg^{9}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [20] v3_op1_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{12}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{10}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [21] v3_op2_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{13}\right)} - \left({f_{3}\left(xg^{3}\right)} + {f_{1}\left(xg^{12}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [22] v3_dst_base_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{14}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{13}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [23] v3_dst_addr $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{3}\left(xg^{15}\right)} - \left({f_{4}\left(xg^{14}\right)} + {f_{1}\left(xg^{14}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [24] v3_sum $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{4}\left(xg^{12}\right)} + {f_{4}\left(xg^{13}\right)} - \left({f_{4}\left(xg^{15}\right)} + {f_{1}\left(xg^{15}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [25] op3_base_addr $${\frac{\left({f_{0}\left(xg^{6}\right)} + {f_{0}\left(xg^{8}\right)} + {f_{0}\left(xg^{10}\right)}\right) \cdot \left({f_{3}\left(xg^{10}\right)} - \left({f_{3}\left(x\right)} + {f_{1}\left(xg^{9}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [26] op3_addr $${\frac{\left({f_{0}\left(xg^{6}\right)} + {f_{0}\left(xg^{8}\right)} + {f_{0}\left(xg^{10}\right)}\right) \cdot \left({f_{3}\left(xg^{11}\right)} - \left({f_{4}\left(xg^{10}\right)} + {f_{1}\left(xg^{10}\right)} - {32768}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [27] cnt_init $${\frac{{f_{3}\left(x\right)} - \mathrm{cnt\_init}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [28] cnt_final $${\frac{{f_{3}\left(x\right)} - \mathrm{cnt\_final}}{{x}^{{\frac{T}{T}}} - {g}^{T - {16}}}}$$

## [29] cnt -> cnt $${\frac{{f_{3}\left(x\right)} - {f_{4}\left(x\right)}}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [30] cnt update $${\frac{\left({f_{3}\left(xg^{16}\right)} - \left({f_{3}\left(x\right)} + \left({1} - {f_{0}\left(xg^{4}\right)}\right) \cdot \left({f_{1}\left(xg^{11}\right)} - {32768}\right) + {f_{0}\left(xg^{4}\right)} \cdot \left({f_{0}\left(xg^{15}\right)} \cdot 2^{4}+{f_{0}\left(xg^{11}\right)} \cdot 2^{3}+{f_{0}\left(xg^{7}\right)} \cdot 2^{2}+{f_{0}\left(xg^{3}\right)} \cdot 2^{1}\right)\right)\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [31] rbp_addr $${\frac{{f_{3}\left(xg\right)} - \left({f_{3}\left(x\right)} + {1}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [32] pc_addr $${\frac{{f_{3}\left(xg^{2}\right)} - \left({f_{3}\left(x\right)} + {2}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [33] mul $${\frac{{f_{0}\left(xg\right)} - \left({f_{4}\left(xg^{5}\right)} + {f_{1}\left(xg^{2}\right)} - {32768}\right) \cdot \left({f_{4}\left(xg^{7}\right)} + {f_{1}\left(xg^{5}\right)} - {32768}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [34] res $${\frac{\left({1} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right)\right)\right) \cdot {f_{0}\left(xg^{5}\right)} - \left({f_{0}\left(x\right)} \cdot {f_{0}\left(xg\right)} + {f_{0}\left(xg^{2}\right)} \cdot \left({f_{4}\left(xg^{5}\right)} + {f_{1}\left(xg^{2}\right)} - {32768} + \left({f_{4}\left(xg^{7}\right)} + {f_{1}\left(xg^{5}\right)} - {32768}\right)\right) + {f_{0}\left(xg^{6}\right)} \cdot {f_{4}\left(xg^{11}\right)} - {f_{0}\left(xg^{8}\right)} \cdot {f_{4}\left(xg^{11}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [35] dst = res if not jnz $${\frac{\left({1} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right) + {f_{0}\left(xg^{4}\right)}\right)\right) \cdot \left({f_{4}\left(xg^{9}\right)} + {f_{1}\left(xg^{8}\right)} - {32768} - {f_{0}\left(xg^{5}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [36] t0 $${\frac{{f_{0}\left(xg^{9}\right)} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right)\right) \cdot \left({f_{4}\left(xg^{5}\right)} + {f_{1}\left(xg^{2}\right)} - {32768}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [37] t1 $${\frac{{f_{0}\left(xg^{13}\right)} - {f_{0}\left(xg^{9}\right)} \cdot {f_{0}\left(xg^{5}\right)}}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [38] jnz fallback $${\frac{\left({f_{0}\left(xg^{13}\right)} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right)\right)\right) \cdot \left({f_{3}\left(xg^{19}\right)} - \left({f_{4}\left(xg^{9}\right)} + {f_{1}\left(xg^{8}\right)} - {32768}\right)\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [39] jnz jump $${\frac{{f_{0}\left(xg^{9}\right)} \cdot \left({f_{3}\left(xg^{19}\right)} - \left({f_{4}\left(xg^{7}\right)} + {f_{1}\left(xg^{5}\right)} - {32768}\right)\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [40] next_pc $${\frac{\left({1} - \left({1} - \left({f_{0}\left(x\right)} + {f_{0}\left(xg^{2}\right)} + {f_{0}\left(xg^{4}\right)}\right)\right)\right) \cdot \left({f_{3}\left(xg^{19}\right)} - \left({f_{3}\left(xg^{3}\right)} + {1}\right)\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [41] next_rbp $${\frac{\left({f_{3}\left(xg^{9}\right)} - {f_{3}\left(xg^{17}\right)}\right) \cdot \left({f_{4}\left(xg^{17}\right)} - {f_{4}\left(xg\right)}\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [42] next_rbp vadd3 $${\frac{{f_{0}\left(xg^{4}\right)} \cdot \left({f_{4}\left(xg^{17}\right)} - {f_{4}\left(xg\right)}\right) \cdot \left(x - {g}^{T - {16}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [43] lo_lo16 $${\frac{{f_{0}\left(xg^{12}\right)} \cdot \left({f_{4}\left(xg^{12}\right)} - {f_{1}\left(xg^{12}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [44] lo_hi16 $${\frac{{f_{0}\left(xg^{12}\right)} \cdot \left({f_{4}\left(xg^{13}\right)} - {f_{1}\left(xg^{13}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [45] hi_lo16 $${\frac{{f_{0}\left(xg^{12}\right)} \cdot \left({f_{4}\left(xg^{14}\right)} - {f_{1}\left(xg^{14}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [46] hi_hi16 $${\frac{{f_{0}\left(xg^{12}\right)} \cdot \left({f_{4}\left(xg^{15}\right)} - {f_{1}\left(xg^{15}\right)}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [47] op3_64 $${\frac{{f_{0}\left(xg^{10}\right)} \cdot \left({f_{4}\left(xg^{11}\right)} - \left({f_{1}\left(xg^{15}\right)} \cdot 2^{64}+{f_{1}\left(xg^{14}\right)} \cdot 2^{48}+{f_{1}\left(xg^{13}\right)} \cdot 2^{32}+{f_{1}\left(xg^{12}\right)} \cdot 2^{16}\right)\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [48] mem_perm_init $${\frac{{z_\mathrm{mem}} - \left({f_{3}\left(x\right)} + {\alpha_\mathrm{mem}} \cdot {f_{4}\left(x\right)}\right) - {f_{23}\left(x\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{5}\left(x\right)} + {\alpha_\mathrm{mem}} \cdot {f_{6}\left(x\right)}\right)\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [49] mem_perm_final $${\frac{{f_{27}\left(xg^{(1/1)T + -2}\right)} - \mathrm{mem\_pub\_final}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [50] mem_addr_min $${\frac{{f_{5}\left(x\right)} - \mathrm{mem\_addr.min}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [51] mem_addr_max $${\frac{{f_{19}\left(xg^{(1/1)T + -2}\right)} - \mathrm{mem\_addr.max}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [52] rc16_perm_init $${\frac{{z_\mathrm{rc16}} - {f_{1}\left(x\right)} - {f_{24}\left(x\right)} \cdot \left({z_\mathrm{rc16}} - {f_{2}\left(x\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [53] rc16_perm_step $${\frac{\left({f_{24}\left(x\right)} \cdot \left({z_\mathrm{rc16}} - {f_{1}\left(xg\right)}\right) - {f_{24}\left(xg\right)} \cdot \left({z_\mathrm{rc16}} - {f_{2}\left(xg\right)}\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [54] rc16_perm_final $${\frac{{f_{24}\left(x\right)} - {1}}{{x}^{{\frac{T}{T}}} - {g}^{T - {1}}}}$$

## [55] rc16_min $${\frac{{f_{2}\left(x\right)} - \mathrm{rc16.min}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [56] rc16_max $${\frac{{f_{2}\left(x\right)} - \mathrm{rc16.max}}{{x}^{{\frac{T}{T}}} - {g}^{T - {1}}}}$$

## [57] s_rc16 is diff-continuous $${\frac{\left({f_{2}\left(xg\right)} - {f_{2}\left(x\right)}\right) \cdot \left({f_{2}\left(xg\right)} - {f_{2}\left(x\right)} - {f_{21}\left(x\right)}\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [58] s_rc16_diff is 2-continuous $${\frac{\left({f_{22}\left(xg\right)} - {f_{22}\left(x\right)}\right) \cdot \left({f_{22}\left(xg\right)} - {2} \cdot {f_{22}\left(x\right)}\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [59] rc16_diff_perm_init $${\frac{{z_{\delta\mathrm{rc16}}} - {f_{21}\left(x\right)} - {f_{28}\left(x\right)} \cdot \left({z_{\delta\mathrm{rc16}}} - {f_{22}\left(x\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [60] rc16_diff_perm_step $${\frac{\left({f_{28}\left(x\right)} \cdot \left({z_{\delta\mathrm{rc16}}} - {f_{21}\left(xg\right)}\right) - {f_{28}\left(xg\right)} \cdot \left({z_{\delta\mathrm{rc16}}} - {f_{22}\left(xg\right)}\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [61] rc16_diff_perm_final $${\frac{{f_{28}\left(x\right)} - {1}}{{x}^{{\frac{T}{T}}} - {g}^{T - {1}}}}$$

## [62] rc16_diff_min $${\frac{{f_{22}\left(x\right)} - \mathrm{rc16\_diff.min}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [63] rc16_diff_max $${\frac{{f_{22}\left(x\right)} - \mathrm{rc16\_diff.max}}{{x}^{{\frac{T}{T}}} - {g}^{T - {1}}}}$$

## [64] s_mem_addr is continuous at 0 $${\frac{\left({\left({f_{5}\left(xg\right)} - {f_{5}\left(x\right)}\right)}^{{2}} - \left({f_{5}\left(xg\right)} - {f_{5}\left(x\right)}\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [65] (s_mem_addr, s_mem_val) is a function at 0 $${\frac{\left({f_{5}\left(xg\right)} - {f_{5}\left(x\right)} - {1}\right) \cdot \left({f_{6}\left(xg\right)} - {f_{6}\left(x\right)}\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [66] mem_perm_step at 0 $${\frac{\left({f_{23}\left(x\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{3}\left(xg\right)} + {\alpha_\mathrm{mem}} \cdot {f_{4}\left(xg\right)}\right)\right) - {f_{23}\left(xg\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{5}\left(xg\right)} + {\alpha_\mathrm{mem}} \cdot {f_{6}\left(xg\right)}\right)\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [67] s_mem_addr is continuous at (1/1)T + -1 $${\frac{{\left({f_{13}\left(xg^{4}\right)} - {f_{5}\left(xg^{(1/1)T + -1}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{4}\right)} - {f_{5}\left(xg^{(1/1)T + -1}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [68] (s_mem_addr, s_mem_val) is a function at (1/1)T + -1 $${\frac{\left({f_{13}\left(xg^{4}\right)} - {f_{5}\left(xg^{(1/1)T + -1}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{12}\right)} - {f_{6}\left(xg^{(1/1)T + -1}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [69] mem_perm_step at (1/1)T + -1 $${\frac{{f_{23}\left(xg^{(1/1)T + -1}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{11}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{11}\left(xg^{108}\right)}\right)\right) - {f_{25}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{4}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{12}\right)}\right)\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [70] s_mem_addr is continuous at (1/1)T + 0 $${\frac{{\left({f_{13}\left(xg^{20}\right)} - {f_{13}\left(xg^{4}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{20}\right)} - {f_{13}\left(xg^{4}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [71] (s_mem_addr, s_mem_val) is a function at (1/1)T + 0 $${\frac{\left({f_{13}\left(xg^{20}\right)} - {f_{13}\left(xg^{4}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{28}\right)} - {f_{13}\left(xg^{12}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [72] mem_perm_step at (1/1)T + 0 $${\frac{{f_{25}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{12}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{12}\left(xg^{108}\right)}\right)\right) - {f_{25}\left(xg^{20}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{20}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{28}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [73] s_mem_addr is continuous at (1/1)T + 1 $${\frac{{\left({f_{13}\left(xg^{36}\right)} - {f_{13}\left(xg^{20}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{36}\right)} - {f_{13}\left(xg^{20}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [74] (s_mem_addr, s_mem_val) is a function at (1/1)T + 1 $${\frac{\left({f_{13}\left(xg^{36}\right)} - {f_{13}\left(xg^{20}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{44}\right)} - {f_{13}\left(xg^{28}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [75] mem_perm_step at (1/1)T + 1 $${\frac{{f_{25}\left(xg^{20}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{108}\right)}\right)\right) - {f_{25}\left(xg^{36}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{36}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{44}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [76] s_mem_addr is continuous at (1/1)T + 2 $${\frac{{\left({f_{13}\left(xg^{52}\right)} - {f_{13}\left(xg^{36}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{52}\right)} - {f_{13}\left(xg^{36}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [77] (s_mem_addr, s_mem_val) is a function at (1/1)T + 2 $${\frac{\left({f_{13}\left(xg^{52}\right)} - {f_{13}\left(xg^{36}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{60}\right)} - {f_{13}\left(xg^{44}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [78] mem_perm_step at (1/1)T + 2 $${\frac{{f_{25}\left(xg^{36}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{11}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{11}\left(xg^{72}\right)}\right)\right) - {f_{25}\left(xg^{52}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{52}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{60}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [79] s_mem_addr is continuous at (1/1)T + 3 $${\frac{{\left({f_{13}\left(xg^{68}\right)} - {f_{13}\left(xg^{52}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{68}\right)} - {f_{13}\left(xg^{52}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [80] (s_mem_addr, s_mem_val) is a function at (1/1)T + 3 $${\frac{\left({f_{13}\left(xg^{68}\right)} - {f_{13}\left(xg^{52}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{76}\right)} - {f_{13}\left(xg^{60}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [81] mem_perm_step at (1/1)T + 3 $${\frac{{f_{25}\left(xg^{52}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{12}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{12}\left(xg^{72}\right)}\right)\right) - {f_{25}\left(xg^{68}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{68}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{76}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [82] s_mem_addr is continuous at (1/1)T + 4 $${\frac{{\left({f_{13}\left(xg^{84}\right)} - {f_{13}\left(xg^{68}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{84}\right)} - {f_{13}\left(xg^{68}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [83] (s_mem_addr, s_mem_val) is a function at (1/1)T + 4 $${\frac{\left({f_{13}\left(xg^{84}\right)} - {f_{13}\left(xg^{68}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{92}\right)} - {f_{13}\left(xg^{76}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [84] mem_perm_step at (1/1)T + 4 $${\frac{{f_{25}\left(xg^{68}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{72}\right)}\right)\right) - {f_{25}\left(xg^{84}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{84}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{92}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [85] s_mem_addr is continuous at (1/1)T + 5 $${\frac{\left({\left({f_{13}\left(xg^{132}\right)} - {f_{13}\left(xg^{84}\right)}\right)}^{{2}} - \left({f_{13}\left(xg^{132}\right)} - {f_{13}\left(xg^{84}\right)}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [86] (s_mem_addr, s_mem_val) is a function at (1/1)T + 5 $${\frac{\left({f_{13}\left(xg^{132}\right)} - {f_{13}\left(xg^{84}\right)} - {1}\right) \cdot \left({f_{13}\left(xg^{140}\right)} - {f_{13}\left(xg^{92}\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [87] mem_perm_step at (1/1)T + 5 $${\frac{\left({f_{25}\left(xg^{84}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{11}\left(xg^{244}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{11}\left(xg^{236}\right)}\right)\right) - {f_{25}\left(xg^{132}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{13}\left(xg^{132}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{13}\left(xg^{140}\right)}\right)\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [88] s_mem_addr is continuous at (67/64)T + -1 $${\frac{{\left({f_{16}\left(xg^{4}\right)} - {f_{13}\left(xg^{(1/1)T + -44}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{4}\right)} - {f_{13}\left(xg^{(1/1)T + -44}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [89] (s_mem_addr, s_mem_val) is a function at (67/64)T + -1 $${\frac{\left({f_{16}\left(xg^{4}\right)} - {f_{13}\left(xg^{(1/1)T + -44}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{12}\right)} - {f_{13}\left(xg^{(1/1)T + -36}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [90] mem_perm_step at (67/64)T + -1 $${\frac{{f_{25}\left(xg^{(1/1)T + -44}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{14}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{14}\left(xg^{108}\right)}\right)\right) - {f_{26}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{4}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{12}\right)}\right)\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [91] s_mem_addr is continuous at (67/64)T + 0 $${\frac{{\left({f_{16}\left(xg^{20}\right)} - {f_{16}\left(xg^{4}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{20}\right)} - {f_{16}\left(xg^{4}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [92] (s_mem_addr, s_mem_val) is a function at (67/64)T + 0 $${\frac{\left({f_{16}\left(xg^{20}\right)} - {f_{16}\left(xg^{4}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{28}\right)} - {f_{16}\left(xg^{12}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [93] mem_perm_step at (67/64)T + 0 $${\frac{{f_{26}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{15}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{15}\left(xg^{108}\right)}\right)\right) - {f_{26}\left(xg^{20}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{20}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{28}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [94] s_mem_addr is continuous at (67/64)T + 1 $${\frac{{\left({f_{16}\left(xg^{36}\right)} - {f_{16}\left(xg^{20}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{36}\right)} - {f_{16}\left(xg^{20}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [95] (s_mem_addr, s_mem_val) is a function at (67/64)T + 1 $${\frac{\left({f_{16}\left(xg^{36}\right)} - {f_{16}\left(xg^{20}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{44}\right)} - {f_{16}\left(xg^{28}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [96] mem_perm_step at (67/64)T + 1 $${\frac{{f_{26}\left(xg^{20}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{116}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{108}\right)}\right)\right) - {f_{26}\left(xg^{36}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{36}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{44}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [97] s_mem_addr is continuous at (67/64)T + 2 $${\frac{{\left({f_{16}\left(xg^{52}\right)} - {f_{16}\left(xg^{36}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{52}\right)} - {f_{16}\left(xg^{36}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [98] (s_mem_addr, s_mem_val) is a function at (67/64)T + 2 $${\frac{\left({f_{16}\left(xg^{52}\right)} - {f_{16}\left(xg^{36}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{60}\right)} - {f_{16}\left(xg^{44}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [99] mem_perm_step at (67/64)T + 2 $${\frac{{f_{26}\left(xg^{36}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{14}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{14}\left(xg^{72}\right)}\right)\right) - {f_{26}\left(xg^{52}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{52}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{60}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [100] s_mem_addr is continuous at (67/64)T + 3 $${\frac{{\left({f_{16}\left(xg^{68}\right)} - {f_{16}\left(xg^{52}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{68}\right)} - {f_{16}\left(xg^{52}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [101] (s_mem_addr, s_mem_val) is a function at (67/64)T + 3 $${\frac{\left({f_{16}\left(xg^{68}\right)} - {f_{16}\left(xg^{52}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{76}\right)} - {f_{16}\left(xg^{60}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [102] mem_perm_step at (67/64)T + 3 $${\frac{{f_{26}\left(xg^{52}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{15}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{15}\left(xg^{72}\right)}\right)\right) - {f_{26}\left(xg^{68}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{68}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{76}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [103] s_mem_addr is continuous at (67/64)T + 4 $${\frac{{\left({f_{16}\left(xg^{84}\right)} - {f_{16}\left(xg^{68}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{84}\right)} - {f_{16}\left(xg^{68}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [104] (s_mem_addr, s_mem_val) is a function at (67/64)T + 4 $${\frac{\left({f_{16}\left(xg^{84}\right)} - {f_{16}\left(xg^{68}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{92}\right)} - {f_{16}\left(xg^{76}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [105] mem_perm_step at (67/64)T + 4 $${\frac{{f_{26}\left(xg^{68}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{124}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{72}\right)}\right)\right) - {f_{26}\left(xg^{84}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{84}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{92}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [106] s_mem_addr is continuous at (67/64)T + 5 $${\frac{\left({\left({f_{16}\left(xg^{132}\right)} - {f_{16}\left(xg^{84}\right)}\right)}^{{2}} - \left({f_{16}\left(xg^{132}\right)} - {f_{16}\left(xg^{84}\right)}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [107] (s_mem_addr, s_mem_val) is a function at (67/64)T + 5 $${\frac{\left({f_{16}\left(xg^{132}\right)} - {f_{16}\left(xg^{84}\right)} - {1}\right) \cdot \left({f_{16}\left(xg^{140}\right)} - {f_{16}\left(xg^{92}\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [108] mem_perm_step at (67/64)T + 5 $${\frac{\left({f_{26}\left(xg^{84}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{14}\left(xg^{244}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{14}\left(xg^{236}\right)}\right)\right) - {f_{26}\left(xg^{132}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{16}\left(xg^{132}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{16}\left(xg^{140}\right)}\right)\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [109] s_mem_addr is continuous at (35/32)T + -1 $${\frac{{\left({f_{20}\left(xg^{11}\right)} - {f_{16}\left(xg^{(1/1)T + -44}\right)}\right)}^{{2}} - \left({f_{20}\left(xg^{11}\right)} - {f_{16}\left(xg^{(1/1)T + -44}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [110] (s_mem_addr, s_mem_val) is a function at (35/32)T + -1 $${\frac{\left({f_{20}\left(xg^{11}\right)} - {f_{16}\left(xg^{(1/1)T + -44}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{15}\right)} - {f_{16}\left(xg^{(1/1)T + -36}\right)}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [111] mem_perm_step at (35/32)T + -1 $${\frac{{f_{26}\left(xg^{(1/1)T + -44}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{3}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{7}\right)}\right)\right) - {f_{27}\left(xg^{3}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{11}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{15}\right)}\right)\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [112] s_mem_addr is continuous at (35/32)T + 0 $${\frac{{\left({f_{20}\left(xg^{27}\right)} - {f_{20}\left(xg^{11}\right)}\right)}^{{2}} - \left({f_{20}\left(xg^{27}\right)} - {f_{20}\left(xg^{11}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [113] (s_mem_addr, s_mem_val) is a function at (35/32)T + 0 $${\frac{\left({f_{20}\left(xg^{27}\right)} - {f_{20}\left(xg^{11}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{31}\right)} - {f_{20}\left(xg^{15}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [114] mem_perm_step at (35/32)T + 0 $${\frac{{f_{27}\left(xg^{3}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{19}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{23}\right)}\right)\right) - {f_{27}\left(xg^{7}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{27}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{31}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [115] s_mem_addr is continuous at (35/32)T + 1 $${\frac{{\left({f_{20}\left(xg^{43}\right)} - {f_{20}\left(xg^{27}\right)}\right)}^{{2}} - \left({f_{20}\left(xg^{43}\right)} - {f_{20}\left(xg^{27}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [116] (s_mem_addr, s_mem_val) is a function at (35/32)T + 1 $${\frac{\left({f_{20}\left(xg^{43}\right)} - {f_{20}\left(xg^{27}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{47}\right)} - {f_{20}\left(xg^{31}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [117] mem_perm_step at (35/32)T + 1 $${\frac{{f_{27}\left(xg^{7}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{35}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{39}\right)}\right)\right) - {f_{27}\left(xg^{11}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{43}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{47}\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [118] s_mem_addr is continuous at (35/32)T + 2 $${\frac{{\left({f_{19}\left(x\right)} - {f_{20}\left(xg^{43}\right)}\right)}^{{2}} - \left({f_{19}\left(x\right)} - {f_{20}\left(xg^{43}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [119] (s_mem_addr, s_mem_val) is a function at (35/32)T + 2 $${\frac{\left({f_{19}\left(x\right)} - {f_{20}\left(xg^{43}\right)} - {1}\right) \cdot \left({f_{20}\left(x\right)} - {f_{20}\left(xg^{47}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [120] mem_perm_step at (35/32)T + 2 $${\frac{{f_{27}\left(xg^{11}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{17}\left(x\right)} + {\alpha_\mathrm{mem}} \cdot {f_{18}\left(x\right)}\right)\right) - {f_{27}\left(x\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{19}\left(x\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(x\right)}\right)\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [121] s_mem_addr is continuous at (35/32)T + $${\frac{\left({\left({f_{19}\left(xg\right)} - {f_{19}\left(x\right)}\right)}^{{2}} - \left({f_{19}\left(xg\right)} - {f_{19}\left(x\right)}\right)\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{2} \cdot T}{{4}}}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [122] (s_mem_addr, s_mem_val) is a function at (35/32)T + $${\frac{\left({f_{19}\left(xg\right)} - {f_{19}\left(x\right)} - {1}\right) \cdot \left({f_{20}\left(xg\right)} - {f_{20}\left(x\right)}\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{2} \cdot T}{{4}}}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [123] mem_perm_step at (35/32)T + $${\frac{\left({f_{27}\left(x\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{17}\left(xg\right)} + {\alpha_\mathrm{mem}} \cdot {f_{18}\left(xg\right)}\right)\right) - {f_{27}\left(xg\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{19}\left(xg\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg\right)}\right)\right)\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{2} \cdot T}{{4}}}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [124] s_mem_addr is continuous at (35/32)T + $${\frac{\left({\left({f_{19}\left(xg^{4}\right)} - {f_{19}\left(xg^{2}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{4}\right)} - {f_{19}\left(xg^{2}\right)}\right)\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [125] (s_mem_addr, s_mem_val) is a function at (35/32)T + $${\frac{\left({f_{19}\left(xg^{4}\right)} - {f_{19}\left(xg^{2}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{4}\right)} - {f_{20}\left(xg^{2}\right)}\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [126] mem_perm_step at (35/32)T + $${\frac{\left({f_{27}\left(xg^{2}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{17}\left(xg^{4}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{18}\left(xg^{4}\right)}\right)\right) - {f_{27}\left(xg^{4}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{19}\left(xg^{4}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{4}\right)}\right)\right)\right) \cdot {1} \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [127] s_mem_addr is continuous at (35/32)T + 98 $${\frac{\left({\left({f_{20}\left(xg^{139}\right)} - {f_{19}\left(xg^{126}\right)}\right)}^{{2}} - \left({f_{20}\left(xg^{139}\right)} - {f_{19}\left(xg^{126}\right)}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [128] (s_mem_addr, s_mem_val) is a function at (35/32)T + 98 $${\frac{\left({f_{20}\left(xg^{139}\right)} - {f_{19}\left(xg^{126}\right)} - {1}\right) \cdot \left({f_{20}\left(xg^{143}\right)} - {f_{20}\left(xg^{126}\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [129] mem_perm_step at (35/32)T + 98 $${\frac{\left({f_{27}\left(xg^{126}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{131}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{135}\right)}\right)\right) - {f_{27}\left(xg^{131}\right)} \cdot \left({z_\mathrm{mem}} - \left({f_{20}\left(xg^{139}\right)} + {\alpha_\mathrm{mem}} \cdot {f_{20}\left(xg^{143}\right)}\right)\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [130] load_const first $${\frac{{f_{7}\left(x\right)} - {1}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [131] load_const can decrease by bit $${\frac{\left({\left({f_{7}\left(x\right)} - {f_{7}\left(xg\right)}\right)}^{{2}} - \left({f_{7}\left(x\right)} - {f_{7}\left(xg\right)}\right)\right) \cdot \left(x - {g}^{T - {1}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [132] load_const last $${\frac{{f_{7}\left(xg^{127}\right)} - {1}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [133] load_const addresses strictly increasing $${\frac{{f_{5}\left(xg^{383}\right)} - {f_{5}\left(x\right)} - {383}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [134] r1 init $${\frac{{f_{7}\left(x\right)} \cdot \left({f_{8}\left(x\right)} - {f_{6}\left(x\right)}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [135] r2 init $${\frac{{f_{7}\left(x\right)} \cdot \left({f_{9}\left(x\right)} - {f_{6}\left(xg^{128}\right)}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [136] r3 init $${\frac{{f_{7}\left(x\right)} \cdot \left({f_{10}\left(x\right)} - {f_{6}\left(xg^{256}\right)}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [137] r1 is periodic $${\frac{\left({f_{8}\left(xg^{128}\right)} - {f_{8}\left(x\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [138] r2 is periodic $${\frac{\left({f_{9}\left(xg^{128}\right)} - {f_{9}\left(x\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [139] r3 is periodic $${\frac{\left({f_{10}\left(xg^{128}\right)} - {f_{10}\left(x\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [140] hash1-hash_start $${\frac{{f_{11}\left(xg^{116}\right)} - \left(\mathrm{hash\_start} + 0 \cdot {6} \cdot {\frac{T}{{128}}}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [141] hash1-in2_addr = in1_addr + 1 $${\frac{{f_{12}\left(xg^{116}\right)} - {f_{11}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [142] hash1-in3_addr = in2_addr + 1 $${\frac{{f_{13}\left(xg^{116}\right)} - {f_{12}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [143] hash1-out1_addr = in3_addr + 1 $${\frac{{f_{11}\left(xg^{124}\right)} - {f_{13}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [144] hash1-out2_addr = out1_addr + 1 $${\frac{{f_{12}\left(xg^{124}\right)} - {f_{11}\left(xg^{124}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [145] hash1-out3_addr = out2_addr + 1 $${\frac{{f_{13}\left(xg^{124}\right)} - {f_{12}\left(xg^{124}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [146] hash1-next_in1_addr = out3_addr + 1 $${\frac{\left({f_{11}\left(xg^{244}\right)} - {f_{13}\left(xg^{124}\right)} - {1}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [147] hash1-pre_round_1 $${\frac{{f_{11}\left(x\right)} - \left({f_{11}\left(xg^{108}\right)} \cdot {2} + {f_{12}\left(xg^{108}\right)} \cdot {1} + {f_{13}\left(xg^{108}\right)} \cdot {1}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [148] hash1-pre_round_2 $${\frac{{f_{12}\left(x\right)} - \left({f_{11}\left(xg^{108}\right)} \cdot {1} + {f_{12}\left(xg^{108}\right)} \cdot {2} + {f_{13}\left(xg^{108}\right)} \cdot {1}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [149] hash1-pre_round_3 $${\frac{{f_{13}\left(x\right)} - \left({f_{11}\left(xg^{108}\right)} \cdot {1} + {f_{12}\left(xg^{108}\right)} \cdot {1} + {f_{13}\left(xg^{108}\right)} \cdot {2}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [150] hash1-hash_full_1_sq $${\frac{\left({f_{25}\left(x\right)} - {\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [151] hash1-hash_full_2_sq $${\frac{\left({f_{11}\left(xg^{4}\right)} - {\left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [152] hash1-hash_full_3_sq $${\frac{\left({f_{12}\left(xg^{4}\right)} - {\left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [153] hash1-hash_full_next1 $${\frac{\left({f_{11}\left(xg^{16}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {2} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{11}\left(xg^{4}\right)} \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{12}\left(xg^{4}\right)} \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [154] hash1-hash_full_next2 $${\frac{\left({f_{12}\left(xg^{16}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{11}\left(xg^{4}\right)} \cdot {2} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{12}\left(xg^{4}\right)} \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [155] hash1-hash_full_next3 $${\frac{\left({f_{13}\left(xg^{16}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{11}\left(xg^{4}\right)} \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{12}\left(xg^{4}\right)} \cdot {2}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [156] hash1-hash_part_1_sq $${\frac{\left({f_{25}\left(x\right)} - {\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [157] hash1-hash_part_next1-continuation $${\frac{\left({f_{11}\left(xg\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {2} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [158] hash1-hash_part_next1-jump $${\frac{\left({f_{11}\left(xg^{2}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {2} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$

## [159] hash1-hash_part_next2-continuation $${\frac{\left({f_{12}\left(xg\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {2} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [160] hash1-hash_part_next2-jump $${\frac{\left({f_{12}\left(xg^{2}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {2} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$

## [161] hash1-hash_part_next3-continuation $${\frac{\left({f_{13}\left(xg\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {3}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [162] hash1-hash_part_next3-jump $${\frac{\left({f_{13}\left(xg^{2}\right)} - \left(\left({f_{11}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{25}\left(x\right)} \cdot {1} + \left({f_{12}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{13}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {3}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$

## [163] hash1-hash_part_start1 $${\frac{{f_{11}\left(xg^{64}\right)} - {f_{11}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [164] hash1-hash_part_start2 $${\frac{{f_{12}\left(xg^{64}\right)} - {f_{12}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [165] hash1-hash_part_start3 $${\frac{{f_{13}\left(xg^{64}\right)} - {f_{13}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [166] hash1-hash_part_end1 $${\frac{{f_{11}\left(xg^{111}\right)} - {f_{11}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [167] hash1-hash_part_end2 $${\frac{{f_{12}\left(xg^{111}\right)} - {f_{12}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [168] hash1-hash_part_end3 $${\frac{{f_{13}\left(xg^{111}\right)} - {f_{13}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [169] hash2-hash_start $${\frac{{f_{14}\left(xg^{116}\right)} - \left(\mathrm{hash\_start} + {1} \cdot {6} \cdot {\frac{T}{{128}}}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [170] hash2-hash_end $${\frac{{f_{14}\left(xg^{(1/1)T + -12}\right)} - \left(\mathrm{hash\_end} - {6}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [171] hash2-in2_addr = in1_addr + 1 $${\frac{{f_{15}\left(xg^{116}\right)} - {f_{14}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [172] hash2-in3_addr = in2_addr + 1 $${\frac{{f_{16}\left(xg^{116}\right)} - {f_{15}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [173] hash2-out1_addr = in3_addr + 1 $${\frac{{f_{14}\left(xg^{124}\right)} - {f_{16}\left(xg^{116}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [174] hash2-out2_addr = out1_addr + 1 $${\frac{{f_{15}\left(xg^{124}\right)} - {f_{14}\left(xg^{124}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [175] hash2-out3_addr = out2_addr + 1 $${\frac{{f_{16}\left(xg^{124}\right)} - {f_{15}\left(xg^{124}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [176] hash2-next_in1_addr = out3_addr + 1 $${\frac{\left({f_{14}\left(xg^{244}\right)} - {f_{16}\left(xg^{124}\right)} - {1}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [177] hash2-pre_round_1 $${\frac{{f_{14}\left(x\right)} - \left({f_{14}\left(xg^{108}\right)} \cdot {2} + {f_{15}\left(xg^{108}\right)} \cdot {1} + {f_{16}\left(xg^{108}\right)} \cdot {1}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [178] hash2-pre_round_2 $${\frac{{f_{15}\left(x\right)} - \left({f_{14}\left(xg^{108}\right)} \cdot {1} + {f_{15}\left(xg^{108}\right)} \cdot {2} + {f_{16}\left(xg^{108}\right)} \cdot {1}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [179] hash2-pre_round_3 $${\frac{{f_{16}\left(x\right)} - \left({f_{14}\left(xg^{108}\right)} \cdot {1} + {f_{15}\left(xg^{108}\right)} \cdot {1} + {f_{16}\left(xg^{108}\right)} \cdot {2}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [180] hash2-hash_full_1_sq $${\frac{\left({f_{26}\left(x\right)} - {\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [181] hash2-hash_full_2_sq $${\frac{\left({f_{14}\left(xg^{4}\right)} - {\left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [182] hash2-hash_full_3_sq $${\frac{\left({f_{15}\left(xg^{4}\right)} - {\left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [183] hash2-hash_full_next1 $${\frac{\left({f_{14}\left(xg^{16}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {2} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{14}\left(xg^{4}\right)} \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{15}\left(xg^{4}\right)} \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [184] hash2-hash_full_next2 $${\frac{\left({f_{15}\left(xg^{16}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{14}\left(xg^{4}\right)} \cdot {2} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{15}\left(xg^{4}\right)} \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [185] hash2-hash_full_next3 $${\frac{\left({f_{16}\left(xg^{16}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {f_{14}\left(xg^{4}\right)} \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {f_{15}\left(xg^{4}\right)} \cdot {2}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{104} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{8}}}} - {1}}}$$

## [186] hash2-hash_part_1_sq $${\frac{\left({f_{26}\left(x\right)} - {\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right)}^{{2}}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [187] hash2-hash_part_next1-continuation $${\frac{\left({f_{14}\left(xg\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {2} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [188] hash2-hash_part_next1-jump $${\frac{\left({f_{14}\left(xg^{2}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {2} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$

## [189] hash2-hash_part_next2-continuation $${\frac{\left({f_{15}\left(xg\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {2} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [190] hash2-hash_part_next2-jump $${\frac{\left({f_{15}\left(xg^{2}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {2} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {1}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$

## [191] hash2-hash_part_next3-continuation $${\frac{\left({f_{16}\left(xg\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {3}\right)\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {1}\right) \cdot \left({x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}\right)}{{x}^{{\frac{T}{{1}}}} - {1}}}$$

## [192] hash2-hash_part_next3-jump $${\frac{\left({f_{16}\left(xg^{2}\right)} - \left(\left({f_{14}\left(x\right)} + {f_{8}\left(x\right)}\right) \cdot {f_{26}\left(x\right)} \cdot {1} + \left({f_{15}\left(x\right)} + {f_{9}\left(x\right)}\right) \cdot {1} + \left({f_{16}\left(x\right)} + {f_{10}\left(x\right)}\right) \cdot {3}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{127} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {g}^{{\frac{{3} \cdot T}{{4}}}}}}$$

## [193] hash2-hash_part_start1 $${\frac{{f_{14}\left(xg^{64}\right)} - {f_{14}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [194] hash2-hash_part_start2 $${\frac{{f_{15}\left(xg^{64}\right)} - {f_{15}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [195] hash2-hash_part_start3 $${\frac{{f_{16}\left(xg^{64}\right)} - {f_{16}\left(xg\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [196] hash2-hash_part_end1 $${\frac{{f_{14}\left(xg^{111}\right)} - {f_{14}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [197] hash2-hash_part_end2 $${\frac{{f_{15}\left(xg^{111}\right)} - {f_{15}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [198] hash2-hash_part_end3 $${\frac{{f_{16}\left(xg^{111}\right)} - {f_{16}\left(xg^{8}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [199] vx1-vx_start $${\frac{{f_{20}\left(xg^{3}\right)} - \mathrm{vx\_start}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [200] vx1-vx_end $${\frac{{f_{20}\left(xg^{(1/1)T + -125}\right)} - \left(\mathrm{vx\_end} - {3}\right)}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [201] vx1-count_nz = count * count_inv $${\frac{{f_{20}\left(xg^{55}\right)} - {f_{19}\left(xg^{127}\right)} \cdot {f_{20}\left(xg^{51}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [202] vx1-vx_in2_addr = vx_in1_addr + 1 $${\frac{{f_{20}\left(xg^{19}\right)} - {f_{20}\left(xg^{3}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [203] vx1-vx_out_addr = vx_in2_addr + 1 $${\frac{{f_{20}\left(xg^{35}\right)} - {f_{20}\left(xg^{19}\right)} - {1}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [204] vx1-vx_next_in1_addr = vx_out_addr + 1 if count = 0 $${\frac{\left({1} - {f_{20}\left(xg^{55}\right)}\right) \cdot \left({f_{20}\left(xg^{131}\right)} - {f_{20}\left(xg^{35}\right)} - {1}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [205] vx1-vx_next_in1_addr = vx_in1_addr if count != 0 $${\frac{{f_{19}\left(xg^{127}\right)} \cdot \left({f_{20}\left(xg^{131}\right)} - {f_{20}\left(xg^{3}\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [206] vx1-vx_f_mul copied $${\frac{\left({f_{17}\left(xg^{7}\right)} - {f_{17}\left(xg^{3}\right)}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [207] vx1-vx_f_mul is bit $${\frac{{{f_{17}\left(xg^{3}\right)}}^{{2}} - {f_{17}\left(xg^{3}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [208] vx1-v2_count_zero is bit $${\frac{{{f_{20}\left(xg^{75}\right)}}^{{2}} - {f_{20}\left(xg^{75}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [209] vx1-v3_count_zero is bit $${\frac{{{f_{20}\left(xg^{79}\right)}}^{{2}} - {f_{20}\left(xg^{79}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [210] vx1-vx_v1_diff_chain_start is bit $${\frac{{{f_{19}\left(xg^{3}\right)}}^{{2}} - {f_{19}\left(xg^{3}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [211] vx1-vx_v1_diff_chain_diff is bit $${\frac{\left({\left({f_{19}\left(xg^{19}\right)} - {2} \cdot {f_{19}\left(xg^{3}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{19}\right)} - {2} \cdot {f_{19}\left(xg^{3}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [212] vx1-vx_v2_diff_chain_start is bit $${\frac{{{f_{19}\left(xg^{7}\right)}}^{{2}} - {f_{19}\left(xg^{7}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [213] vx1-vx_v2_diff_chain_diff is bit $${\frac{\left({\left({f_{19}\left(xg^{23}\right)} - {2} \cdot {f_{19}\left(xg^{7}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{23}\right)} - {2} \cdot {f_{19}\left(xg^{7}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [214] vx1-vx_v3_diff_chain_start is bit $${\frac{{{f_{19}\left(xg^{11}\right)}}^{{2}} - {f_{19}\left(xg^{11}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [215] vx1-vx_v3_diff_chain_diff is bit $${\frac{\left({\left({f_{19}\left(xg^{27}\right)} - {2} \cdot {f_{19}\left(xg^{11}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{27}\right)} - {2} \cdot {f_{19}\left(xg^{11}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [216] vx1-vx_count_start is bit $${\frac{{{f_{19}\left(xg^{15}\right)}}^{{2}} - {f_{19}\left(xg^{15}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [217] vx1-vx_count_chain_diff is bit $${\frac{\left({\left({f_{19}\left(xg^{31}\right)} - {2} \cdot {f_{19}\left(xg^{15}\right)}\right)}^{{2}} - \left({f_{19}\left(xg^{31}\right)} - {2} \cdot {f_{19}\left(xg^{15}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{112} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{16}}}} - {1}}}$$

## [218] vx1-vx v1_begin $${\frac{{f_{20}\left(xg^{79}\right)} \cdot {\mathrm{400000000000000000000}_{16}} + {f_{20}\left(xg^{75}\right)} \cdot {\mathrm{200000000000000000000}_{16}} + {f_{17}\left(xg^{3}\right)} \cdot {\mathrm{100000000000000000000}_{16}} + {f_{19}\left(xg^{127}\right)} \cdot {\mathrm{1000000000000000000}_{16}} + {f_{19}\left(xg^{115}\right)} \cdot {\mathrm{10000000000000000}_{16}} + {f_{17}\left(x\right)} - {f_{20}\left(xg^{63}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [219] vx1-vx v2_begin $${\frac{\left({1} - {f_{20}\left(xg^{75}\right)}\right) \cdot {f_{19}\left(xg^{127}\right)} \cdot {\mathrm{1000000000000000000}_{16}} + {f_{19}\left(xg^{119}\right)} \cdot {\mathrm{10000000000000000}_{16}} + {f_{17}\left(xg\right)} - {f_{20}\left(xg^{67}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [220] vx1-vx v3_begin $${\frac{\left({1} - {f_{20}\left(xg^{79}\right)}\right) \cdot {f_{19}\left(xg^{127}\right)} \cdot {\mathrm{1000000000000000000}_{16}} + {f_{19}\left(xg^{123}\right)} \cdot {\mathrm{10000000000000000}_{16}} + {f_{17}\left(xg^{2}\right)} - {f_{20}\left(xg^{71}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [221] vx1-vx v1_stride $${\frac{{f_{17}\left(xg^{4}\right)} - {f_{17}\left(x\right)} - {f_{19}\left(xg^{115}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [222] vx1-vx v2_stride $${\frac{{f_{17}\left(xg^{5}\right)} - {f_{17}\left(xg\right)} - {f_{19}\left(xg^{119}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [223] vx1-vx v3_stride $${\frac{{f_{17}\left(xg^{6}\right)} - {f_{17}\left(xg^{2}\right)} - {f_{19}\left(xg^{123}\right)}}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [224] vx1-vx product $${\frac{{f_{18}\left(xg^{3}\right)} - {f_{18}\left(x\right)} \cdot {f_{18}\left(xg\right)}}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [225] vx1-vx result $${\frac{{f_{18}\left(xg^{2}\right)} - \left({f_{17}\left(xg^{3}\right)} \cdot {f_{18}\left(xg^{3}\right)} + \left({1} - {f_{17}\left(xg^{3}\right)}\right) \cdot \left({f_{18}\left(x\right)} + {f_{18}\left(xg\right)}\right)\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [226] vx1-vx in1_continue internal $${\frac{{f_{19}\left(xg^{127}\right)} \cdot \left({f_{20}\left(xg^{191}\right)} - \left({f_{20}\left(xg^{63}\right)} + {f_{19}\left(xg^{115}\right)} \cdot {32} - {\mathrm{1000000000000000000}_{16}}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [227] vx1-vx in2_continue internal $${\frac{{f_{19}\left(xg^{127}\right)} \cdot \left({f_{20}\left(xg^{195}\right)} - \left({f_{20}\left(xg^{67}\right)} + {f_{19}\left(xg^{119}\right)} \cdot {32} - \left({1} - {f_{20}\left(xg^{75}\right)}\right) \cdot {\mathrm{1000000000000000000}_{16}}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [228] vx1-vx out_continue internal $${\frac{{f_{19}\left(xg^{127}\right)} \cdot \left({f_{20}\left(xg^{199}\right)} - \left({f_{20}\left(xg^{71}\right)} + {f_{19}\left(xg^{123}\right)} \cdot {32} - \left({1} - {f_{20}\left(xg^{79}\right)}\right) \cdot {\mathrm{1000000000000000000}_{16}}\right)\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [229] vx1-vx in1_step $${\frac{\left({1} - {f_{20}\left(xg^{59}\right)}\right) \cdot \left({f_{20}\left(xg^{63}\right)} - {f_{20}\left(xg^{7}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [230] vx1-vx in2_step $${\frac{\left({1} - {f_{20}\left(xg^{59}\right)}\right) \cdot \left({f_{20}\left(xg^{67}\right)} - {f_{20}\left(xg^{23}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [231] vx1-vx out_step $${\frac{\left({1} - {f_{20}\left(xg^{59}\right)}\right) \cdot \left({f_{20}\left(xg^{71}\right)} - {f_{20}\left(xg^{39}\right)}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [232] vx1-first prev_count_nz is zero $${\frac{{f_{20}\left(xg^{59}\right)}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [233] vx1-prev_count_nz is copied $${\frac{\left({f_{20}\left(xg^{187}\right)} - {f_{19}\left(xg^{127}\right)}\right) \cdot \left(x - {g}^{T - {128}}\right)}{{x}^{{\frac{T}{{128}}}} - {1}}}$$

## [234] vx1-vx last_count is zero $${\frac{{f_{19}\left(xg^{(1/1)T + -1}\right)}}{{x}^{{\frac{T}{T}}} - {1}}}$$

## [235] vx1-vx v1_addr is arithmetic $${\frac{\left({f_{17}\left(xg^{8}\right)} - {f_{17}\left(xg^{4}\right)} - \left({f_{17}\left(xg^{4}\right)} - {f_{17}\left(x\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [236] vx1-vx v2_addr is arithmetic $${\frac{\left({f_{17}\left(xg^{9}\right)} - {f_{17}\left(xg^{5}\right)} - \left({f_{17}\left(xg^{5}\right)} - {f_{17}\left(xg\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$

## [237] vx1-vx v3_addr is arithmetic $${\frac{\left({f_{17}\left(xg^{10}\right)} - {f_{17}\left(xg^{6}\right)} - \left({f_{17}\left(xg^{6}\right)} - {f_{17}\left(xg^{2}\right)}\right)\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{120} \cdot T}{{128}}}}\right) \cdot \left({x}^{{\frac{T}{{128}}}} - {g}^{{\frac{{124} \cdot T}{{128}}}}\right)}{{x}^{{\frac{T}{{4}}}} - {1}}}$$